J. Hydrol. Hydromech., 62, 2014, 3, 218–225
DOI: 10.2478/johh-2014-0024
The joint probability distribution of runoff and sediment and its change
characteristics with multi-time scales
Jinping Zhang1*, Zhihong Ding2, Jinjun You3
1
Institute of Water Resources and Environment, Zhengzhou University, High-tech District, No. 100 Science Road, Zhengzhou City,
450001, Henan Province, China.
2
Haihe River Water Conservancy Commission, Tianjin, 300072, China.
3
State Key Laboratory of Hydrologic Cycle Simulation and Regulation, China Institute of Water Resources & Hydropower Research,
Beijing, 100038, China.
*
Corresponding author. Tel.: +86-371-60119629. E-mail: [email protected]
Abstract: River runoff and sediment transport are two related random hydrologic variables. The traditional statistical
analysis method usually requires those two variables to be linearly correlated, and also have an identical marginal
distribution. Therefore, it is difficult to know exactly the characteristics of the runoff and sediment in reality. For this
reason, copulas are applied to construct the joint probability distribution of runoff and sediment in this article. The risk of
synchronous-asynchronous encounter probability of annual rich-poor runoff and sediment is also studied. At last, the
characteristics of annual runoff and sediment with multi-time scales in its joint probability distribution space are
simulated by empirical mode decomposition method. The results show that the copula function can simulate the joint
probability distribution of runoff and sediment of Huaxia hydrological station in Weihe River well, and that such joint
probability distribution has very complex change characteristics at time scales.
Keywords: Runoff; Sediment; Joint probability distribution; Copula; Empirical mode decomposition method.
INTRODUCTION
For the different meteorological factors and underlying
surface conditions, runoff and sediment transport are not
independent of each other. Some attempts have been made to
study the correlations of the random hydrologic variables in the
field of rainfall (i.e., rainfall density, depth, and duration), flood
(i.e., flood peak, volume, and duration) and drought (i.e.,
drought severity, magnitude, and duration), etc. For example,
Correia (1987) studied the joint probability distribution of flood
peak and volume using bivariate normal distribution. Goel et al.
(1998) and Yue (2000) achieved this condition by preliminary
data transformation through Box-Cox’s formulas to represent
the joint probability distribution of peak rainfall intensity and
depth. As early as 1985, Hashino (1985) proposed the Freund
(1961) bivariate exponential distribution to discuss the joint
probability distribution of rainfall intensity and maximum storm
surge. Singh and Singh (1991) described the joint probability
distribution of rainfall intensity and depth with this mathematic
method by using empirical frequency analysis. Han et al. (2007)
and Liu and Chen (2009) investigated the risk of synchronousasynchronous encounter probability of annual rich-poor
precipitation in the East and Middle Routes of South-to-North
Water Transfer Project. Yue (2001), Yue and Rasmussen
(2002), and Yue et al. (1999) applied the Gumbel’s (1960,
1967) distribution for flood and rainfall frequency analysis. Yue
and Wang (2004) constructed the joint risk assessment model to
study the relationships between inflow runoff and rainfall of
Nangang reservoir in the Hutuohe River Basin. Zhou et al.
(2005) verified Gumbel logistic distributions for annual
maximum wind speed and effective wave height.
However, the above mentioned works were based on certain
assumptions, e.g. that all univariates have the same marginal
distributions, and the correlations between variables must be
linear. In practice, most of the random hydrologic variables
cannot meet those assumptions easily. Therefore, copulas which
218
are based on nonlinear relationships among variables and do not
require many assumptions have become prevalent in hydrologic
research. Copula function can decompose the joint distribution
function into univariable marginal distribution functions and a
link function. The flexibility offered by copula for joint
probability distribution construction is evident from the relevant
studies on rainfall frequency analysis (Balistrocchi and Bacchi,
2011; Gyasi-Agyei, 2012; Gyasi-Agyei and Melching, 2012;
Salvatore and Francesco, 2006), flood frequency analysis
(Chowdhary et al., 2011; Renard and Lang, 2007; Salarpour et
al., 2013; Xiao et al., 2008; Xu et al., 2008; Zhang and Singh,
2007), drought frequency analysis (Kao and Govindaraju, 2010;
Ma et al., 2013; Yan et al., 2007), and also the risk analysis of
synchronous-asynchronous encounter probability for annual
rich-poor rainfall or runoff (Ganguli and Reddy, 2013; Lian et
al., 2013; Xiong et al., 2005). Although the prior works have
been done by other researchers, there are still some
undiscovered aspects of the copula applications in hydrology,
especially on the joint probability distribution of runoff and
sediment transport in sandy rivers.
In the study of hydrologic variables with a long time series,
wavelet analysis is an effective method (Compagnucci et al.,
2000; Gaucherel, 2002; Labat et al., 2004; Wang and Meng,
2007). But limited by Fourier transform, the signal must be
stable inside the wavelet window. Although wavelet transform
can get higher resolution in the frequency domain and time
domain, there are still some restrictions in wavelet transform,
which results in many false harmonics. Moreover, the selection
of different wavelet base functions has significant impact on
wavelet analysis. In 1998, Huang et al. (1998) proposed a new
signal analysis method - empirical mode decomposition, and
later made some improvements (Huang et al., 1999). Empirical
mode decomposition method can extract fluctuations or trends
of a signal step by step at different scales (frequency)
simultaneously, which produces data series with different
characteristics-intrinsic
mode
function.
Hilbert-Huang
The joint probability distribution of runoff and sediment and its change characteristics with multi-time scales
C (u 2 , v 2 ) − C (u 2 , v1 ) − C (u1 , v 2 ) + C (u1 , v1 ) ≥ 0
transform, applying Hilbert transform on intrinsic mode
function, is very suitable for nonlinear and non-stationary time
series. Although it is similar to wavelet spectrum, Hilbert
spectrum provides clearer and more detailed partial features.
The key of Hilbert-Huang transform is to get spectra with
higher resolution in time domain and frequency domain. At
present, empirical mode decomposition method has been
successfully applied in turbulence, earthquake research,
atmospheric science and ecology, environment, economy and
other nonlinear areas, but very rarely in hydrology.
The aims of this paper are to (1) get marginal distribution of
runoff and sediment with frequency distribution curve of P-IIItype; (2) construct the joint probability distribution model of
runoff and sediment with copulas; (3) analyze the risk of
synchronous-asynchronous encounter probability of annual
rich-poor runoff and sediment; (4) present the characteristics of
runoff and sediment with multi-time scale in the joint
probability distribution space by empirical mode decomposition
method.
(c) ∀u , v ∈ [0,1]
2
,
max(u + v − 1,0) ≤ C (u, v ) ≤ min(u, v)
The correlation of copula function
The most popular three types of copula functions in
hydrology are shown as Table 1 (Cherubini et al., 2004;
Grimaldi et al., 2005), which belong to the Archimedean copula
family. τ is Kendall’s correlation coefficient. It describes the
nonlinear correlation of variables and can be estimated using the
equation:
τ=
1
 sign[(xi − x j )(yi − y j )]
(2)
C n2 i < j
(
(
(
)(
)(
)(
)
)
)
 1 xi − x j y i − y j > 0
where, sign xi − x j yi − y j =  0 x i − x j y i − y j = 0
− 1 x − x y − y < 0
i
j
i
j

[(
COPULAS
Sklar theorem
Sklar theorem is the basis of copula theory. Suppose there
are two continuous random variables denoted as X and Y , let
F X (x ) and FY ( y ) be the marginal distribution functions of X
)]
)(
Identification and goodness-of-fit evaluation of copula
function
and Y , and F (x, y ) be the joint distribution function. If FX (x )
Using the Kolmogorov-Smirnov test, the appropriate copula
is identified. The identified statistic is given by:
function Cθ (u, v ) exists as b (Nelsen, 1999):

m
m −1 
D = max  C k − k , C k − k

n
n 
1≤k ≤n
and FY ( y ) are continuous, a uniquely determined copula
F (x, y ) = Cθ (FX (x ), FY ( y )) ， ∀ x, y
(1)
(3)
where, Ck is the value of observed (xk , yk ) of the copula
where, Cθ (u, v) is called copula function, θ is parameter to be
determined.
function, mk is the number of observed (xk , yk ) satisfying with
x ≤ xk and y ≤ yk . The goodness-of-fit of copula function is
evaluated by the minimum deviation square) with the following
expression:
The properties of copula function
A bivariate copula function is defined as a mapping
C: [0, 1]2 → [0, 1] with the following properties:
OLS =
∀u , v ∈ [0,1]
C(u,0) = 0 ; C (0, v ) = 0 ;
C(u,1) = u ; C (1, v ) = v ;
(b) ∀ u1 , u 2 , v1 , v 2 ∈ [0,1], u1 ≤ u 2 , v1 ≤ v 2 ,
(a)
1 n
 (Pi − Pei )2
n i =1
(4)
where, Pi is the calculated frequency of the joint probability
distribution, Pei is the empirical frequency of the joint
probability distribution, OLS is the minimum deviation square.
Table 1. Three Archimedean copula families in the field of hydrology research.
Archimedean
Cθ (u , v )
θ ’s range
(u −θ + v −θ − 1) −1 θ
θ >0
copula
Clayton
Frank
Gumbel-Hougaard
−
(
)(
)

e −θu − 1 e −θv − 1 
ln 1 +

θ 
e −θ − 1

1
(
exp  − ( − ln u )θ + ( − ln v )θ

) θ 
1
θ ∈R
θ ≥1
Relation between
τ=
τ = 1−
4 1
−
θ  θ
τ
and
θ
θ
θ +2
t
0

θ exp (t ) − 1 dt − 1
τ = 1−
1
θ
219
Jinping Zhang, Zhihong Ding, Jinjun You
EMPIRICAL MODE DECOMPOSITION METHOD
Intrinsic mode function proposed by Huang must satisfy two
following conditions: (1) In the whole data range, the number of
local extremes and the number of zero-crossings must be equal
or at most have a difference of 1; (2) At any point, the mean
value of the upper envelope formed by all local maxima and the
lower envelope formed by all local minima is zero.
The key step of empirical mode decomposition method is to
extract intrinsic mode function from the given time series x (t ) .
First, the upper envelope and the lower envelope are
constructed by identified local maxima points and local minima
points with a cubic spline interpolation application. Then, the
mean value of the two envelopes is calculated as m1 , and a new
time series removing lower frequency is achieved by:
h1 (t ) = x(t ) − m1
(5)
usually, h1 (t ) is not an expected intrinsic mode function, so we
need to repeat this shifting process k times until the obtained
mean envelopes are zero. At this moment, the final time series
can be shown as:
h1k = h1( k −1) − m1k
(6)
where, h1k is the series of shifting process k times, h1(k −1) is
the series of shifting process k − 1 times. Intrinsic mode
function is evaluated to stop the shifting process by the criterion
of standard deviation value between 0.2~0.3. The criterion of
standard deviation is defined as:
SD =
T

k =1
h1( k −1) (t ) − h1k (t )
h1( k −1) (t ) 2
2
(7)
where, SD is the criterion of standard deviation, T is the
length of the time series. When h1k arrives at the stopping
criterion of standard deviation, we have the first intrinsic mode
function component c1 = h1k from the data x (t ) which
represents the highest frequency component of the original time
series. The residue r1 = x(t) − c1 will be decomposed further
until rn becomes a monotonic function or at most has one local
extreme point. Thus, we get intrinsic mode function modes with
one residue rn . The original series x(t ) is then rewritten as:
n
x(t ) =  ci + rn
Now, each intrinsic mode function component represents a
data series of a characteristic scale (or frequency). In fact, the
empirical mode decomposition method decomposes original
data series into various fluctuations owning different features,
and then superimposes them. Each intrinsic mode function may
be either linear or non-linear, and all decomposed intrinsic
mode function components have the actual corresponding
physical significances.
APPLICATION
Data series
The Weihe River is the largest tributary of the Yellow River
in China. About 55% of runoff comes from the area above the
Xianyang hydrologic station on the mainstream of the Weihe
River, while 80% of sediment is from the Jinghe River, a
tributary of the Weihe River. Huaxian hydrological station,
located 73 km from the river mouth at Goujiabao village (Hua
County, Shaanxi Province), is the main control station of the
lower reaches of the Weihe River. Catchment area is
106,500 km2 (shown as in Fig.1).
Fig. 1. The location of the study site in China.
220
(8)
i =1
100
80
60
40
7
Sediment
Sediment(10 t)
Runoff
Frequency (%)
Fig. 4. Frequency distribution curve of annual sediment.
120
200
180
160
140
120
100
80
60
40
20
0
20
0
1935
1938
1941
1944
1947
1950
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2001
2004
2007
8
3
Runoff（ 10 m ）
The observed runoff and sediment data series of Huaxian
hydrological station used in this article are from 1935 to 2008
(shown as in Fig. 2). These data series are all obtained from the
hydrology bureau of the Yellow River Conservancy
Commission. The hydrology bureau of the Yellow River
Conservancy Commission is the hydrologic authority in the
Yellow River Basin, so the monitoring, collection and disposal
of the hydrological and meteorological information in the whole
Yellow River Basin is one of its main activities. Meanwhile,
because the hydrology bureau of the Yellow River Conservancy
Commission is a pilot unit for the establishment of scientific
data sharing platform in the field of hydrology and water
resources, the hydrological database structure and the data have
passed the national acceptance. Thus, the quality of the
observed runoff and sediment data series of Huaxian
hydrological station used in this paper is well guaranteed.
Sediment (/108t)
The joint probability distribution of runoff and sediment and its change characteristics with multi-time scales
Joint probability distribution of runoff and sediment based
on copulas
According to the above mentioned formulas, Kendall’s
correlation coefficient τ , parameter θ of copula function,
identified statistic D and the minimum deviation square OLS
can be achieved (shown as in Table 2).
year
Table 2. Calculation and evaluation of copula functions.
Fig. 2. The annual runoff and sediment data series at Huaxian
hydrological station.
Kendall’s
P-III-type frequency distribution curve of runoff and
sediment
Hydrologic analysis in China generally assumes the
hydrologic variable subjects to P-III-type distribution. In this
paper, the statistical parameters of runoff frequency distribution
shown in Fig. 3 and sediment frequency distribution shown in
Fig. 4 are obtained by optimal fitting method. We can see that
the mean value x , coefficient of variation Cv and the skewness
coefficient Cs in runoff series are 74.7×108m3/s, 0.48 and 0.79
Runoff (108m3)
separately, while in the sediment series they are 3.47×108m3/s,
0.68 and 1.51.
τ
0.5969
Fig. 3. Frequency distribution curve of annual runoff.
Clayton
Frank
GumbelHougaard
θ
1.3467
4.1942
1.6734
D
0.0636
0.0577
0.0701
OLS
0.02445
0.02246
0.02829
Taking the significance level α = 0 .05 , when n = 74 , the
corresponding fractile value of K-S test is 0.15549, it must not
be less than identified statistic D of undetermined copula
functions. From Table 2, we know that these three copula
functions are all checked by Kolmogorov-Smirnov test with a
small difference of their minimum deviation square values. For
its minimum value of deviation square, Frank copula function is
selected to describe the joint probability distribution of the
runoff and sediment in the lower reaches of the Weihe River.
The selected Frank copula function is expressed as:
F (x, y ) = −
Frequency (%)
Copula functions
Parameter
or index
(
)(
)

1
e −4.1942x − 1 e −4.1942y − 1 
ln1 +

4.1942 
e −4.1942 − 1

(9)
where, F (x) and F (y) are cumulative distribution functions of
runoff and sediment separately.
The goodness-of-fit evaluation of selected Frank copula
function is shown in Fig. 5. The correlation coefficient of Frank
copula-based calculation probability distribution and empirical
probability distribution attains to above 0.99, and all points fall
near the 45° diagonal. It reveals that Frank copula is reasonable.
221
Empirical probability
Jinping Zhang, Zhihong Ding, Jinjun You
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
The return period and risk analysis of synchronousasynchronous encounter probability of annual runoff and
sediment
2
R = 0.9934
Let F (x) and F ( y) be the marginal cumulative distribution
function of runoff ( x ) and sediment ( y ), and F ( x, y) be their
joint distribution function. The synchronous-asynchronous
encounter risk of annual runoff and sediment is denoted as the
return period T . Here, two kinds of return periods are
considered:
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Frank copula-based calculation probability
Fig. 5. The comparison of Frank copula-based calculation
probability with empirical probability.
The frequency analysis of synchronous-asynchronous
encounter situation of annual runoff and sediment
According to the frequency of pf = 37.5％ and pk = 62.5％,
the rich or poor situation of runoff and sediment are classified.
The synchronous-asynchronous encounter situation of annual
rich-poor runoff and sediment are expressed as follows:
1

 T x, y = 1 − F (x, y )

1
T ∗ x, y =

1 − F ( x ) − F ( y ) + F ( x, y )
where, Tx , y is joint return period, indicating that the exceeded
risk of any design variable; T *x, y is simultaneous return period,
indicating the exceeded risk of all design variables.
With the constructed joint probability distribution, the
encounter return periods of runoff and sediment are shown in
Fig. 6 and Fig. 7.
12. 0
Rich-rich encounter frequency:
p1 = P X ≥ x pf , Y ≥ y pf ;
(
)
9. 6
)
Sediment (108t)
p 2 = P X ≥ x pf , y pk < Y < y pf ;
Rich-poor encounter frequency:
p3 = P X ≥ x pf , Y ≤ y pk ;
(
)
Normal-rich encounter frequency:
(
Normal-normal encounter frequency:
(
)
Poor-rich encounter frequency:
p 7 = P X ≤ x pk , Y ≥ y pf ;
)
(
1.2 year
The frequency analysis of synchronous-asynchronous
encounter situation of annual rich-poor runoff and sediment is
displayed in Table 3.
It can be seen that: (1) Synchronous encounter frequency of
annual rich runoff and rich sediment is 24.21%, which is equal
to synchronous encounter frequency of annual poor runoff and
poor sediment. Synchronous encounter frequency of annual
normal runoff and normal sediment is the minimum value of
8.04%; (2) Asynchronous encounter frequency of rich (or poor)
runoff and poor (or rich) sediment is only 4.81% while others
are all 8.48%; (3) The total synchronous encounter frequency is
56.46%.It is larger than that of asynchronous encounter
frequency with the value of 43.54%.
40
60
80
100
3
Runoff (10 m )
Fig. 6. Isopleths map for runoff and sediment of the joint return
periods.
12. 0
10. 8
Sediment (108t)
)
20
8
)
Poor-poor encounter frequency:
p9 = P X ≤ x pk , Y ≤ y pk .
222
1.5 year
4. 8
0
p8 = P X ≤ x pk , y pk < Y < y pf ;
(
2 year
6. 0
1. 2
)
Normal-poor encounter frequency:
p6 = P x pk < X < x pf , Y ≤ y pk ;
Poor-normal encounter frequency:
7. 2
2. 4
p5 = P x pk < X < x pf , y pk < Y < y pf ;
(
3.5 year
8. 4
3. 6
)
p 4 = P x pk < X < x pf , Y ≥ y pf ;
(
20year
10 year
10. 8
Rich-normal encounter frequency:
(
(10)
9. 6
20 year
8. 4
7. 2
10 year
6. 0
4. 8
3. 6
2. 4
0
3.5 year
2 year
1.5 year
1.2 year
20
40
60
80
100
8
120
140
160
180
200
3
Runoff (10 m )
Fig. 7. Isopleths map for runoff and sediment of simultaneous
recurrence periods.
The joint probability distribution of runoff and sediment and its change characteristics with multi-time scales
Table 3. The frequency analysis of synchronous-asynchronous encounter situation of annual rich-poor runoff and sediment (%).
Synchronous frequency
Rich
-rich
Normal
normal
Poor
-poor
24.21
8.04
24.21
Asynchronous frequency
Total
Rich
runoff-normal
sediment
Rich
runoff-poor
sediment
Normal
runoff-poor
sediment
Normal
runoff-rich
sediment
Poor
runoff-rich
sediment
Poor
runoff-normal
sediment
Total
56.46
8.48
4.81
8.48
8.48
4.81
8.48
43.54
The characteristics of annual runoff and sediment with
multi-time scale in its joint probability distribution space
0. 1
Probability
0. 05
0
- 0. 05
- 0. 1
- 0. 15
- 0. 2
1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
Fig. 11. The third intrinsic mode function component.
0. 06
0. 04
0. 02
Probability
In the long time series, the hydrologic variables change at
various time scales (or periods) and the partial fluctuations.
These changes and fluctuation can be decomposed by certain
mathematical method.
The joint probability distribution based on copulas of runoff
and sediment in the lower reaches of the Weihe River is shown
in Fig. 8. Under the assumption that the evaluated criterion of
standard deviation value is 0.25, the probability series is
decomposed by empirical mode decomposition method, and the
border issues are addressed by the boundary extension method.
The decomposed results (shown in Fig. 9–Fig. 13) include four
intrinsic mode function components and one residue. We can
see that: (1) The joint probability distribution of runoff and
sediment can be decomposed into four oscillation components
with various fluctuation periods and a trend component.
0. 15
0
- 0. 02
- 0. 04
Probability
- 0. 06
- 0. 08
1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
Fig. 12. The fourth intrinsic mode function component.
Year
0. 6
Fig. 8. The copula-based joint probability distribution of runoff
and sediment.
0. 55
0. 5
Probability
0. 45
0. 5
0. 4
Probability
0. 3
0. 2
0. 3
0. 25
0. 1
0. 2
0
0. 15
0. 1
1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
- 0. 1
- 0. 2
Year
- 0. 3
Fig. 13. The residual component.
- 0. 4
- 0. 5
1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
Fig. 9. The first intrinsic mode function component.
0. 15
0. 1
Probability
0. 4
0. 35
0. 05
0
- 0. 05
- 0. 1
- 0. 15
- 0. 2
1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
Fig. 10. The second intrinsic mode function component.
It indicates that there has been a complex movement of
runoff and sediment in the lower reaches of the Weihe River.
(2)A quasi-periodic fluctuation of 2 to 4 years is presented in
the first intrinsic mode function component. Larger fluctuations
appeared in the 1930s, then they slowed down from the late
1950s to the early 1990s; (3) A quasi-periodic fluctuation of 4
to 8 years is exhibited in the second intrinsic mode function
component. Larger fluctuations existed in early 1980s, then they
gradually slowed down and began to rise in the beginning of
21st. (4) A quasi-periodic fluctuation of 9 to 11 years is revealed
in the third intrinsic mode function component. The period of
23 years started from the mid-1960s to the late 1980s, and 15
years was found in late 1980s. However, the fluctuation is not
remarkable; (5) In the fourth intrinsic mode function, a quasiperiodic fluctuation of 26 years is in the whole study time scale
with remarkable changes; (6) The residue component indicates
223
Jinping Zhang, Zhihong Ding, Jinjun You
the overall varying trend of the joint probability distribution of
runoff and sediment. The peak value of 0.5244 appears in 1947
and has been decreasing since then.
CONCLUSIONS
The joint probability distribution based on the copulas can
match the runoff and sediment well in the Weihe River, and the
selected Frank copula function is better than others in three
kinds of Archimedean copula functions. In applications with the
constructed joint probability distribution, we can know the
encounter frequencies of runoff and sediment in different state.
The studied results show that the total frequencies of the
synchronous encounter case of annual rich-poor runoff and
sediment are larger than that of the asynchronous encounter
case. Moreover, various recurrence periods’ isopleth maps of
the runoff and sediment encounter case can be obtained
according to the joint probability distribution. If we have an
appropriate distribution process of runoff and sediment of a
typical year, we can implement the same frequency
amplification method to obtain several groups of runoff and
sediment with the same return period. This will provide a
technical support for the planning and regulation of the Weihe
River. The decomposed results by empirical mode
decomposition method reveal that a sophisticated random
motion exists in the lower reaches of the Weihe River, and the
overall trend of joint probability distribution of runoff and
sediment had increased in previous 12 years and then it was
attenuated.
Acknowledgements. This research is supported by the National
Natural Sciences Foundation of China (Project No. 51309202,
51379216, 50939006) and the National Key Basic Research
Project of China (973-2010CB951102), and also by Program for
Innovative Research Team (in Science and Technology) in
University of Henan Province (No. 13IRTSTHN030).
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Received 29 April 2013
Accepted 17 March 2014
Note: Colour version of Figures can be found in the web version of this article.
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